什么是高斯法律:理论与意义

随着科学范围的广泛扩大和各种技术的发展,我们学得越多,获得的知识就越多。我们需要注意的一个关键问题是高斯定律,它分析电荷,除了表面和电荷的概念电量. The law was initially articulated by Lagrange in the year 1773 and then it was supported by Friedrich in 1813. This law is one of the Maxwell proposed four equations where this is a fundamental concept for classical electrodynamics. So, let’s dive more into the concept and know all the related concepts of Gauss law.

What is the Gauss Law?

Gauss law can be defined in both the concepts of magnetic and electric fluxes. In the view of electricity, this law defines that electric flux all through the enclosed surface has direct proportion to the total electrical charge which is enclosed by the surface. It indicates that the insular electrical charges do exist and such similar charges get repelled whereas dissimilar charges get attracted. And in the scenario of magnetism, this law states that magnetic flux all through the enclosed surface is null. And gauss law seems to be stable in the scrutiny that the separated58必威 不存在。这个高斯法律图如下所示:


Gauss Law Diagram
Gauss Law Diagram

该法律可以定义为封闭表面中的净电量等于电荷与介电常数相对应。

Ф电的= q /є0

Where ‘Q’ corresponds to the entire electrical charge inside the closed surface

'♥0'对应电常数因子

这是根本的高斯定律公式.

Gauss Law Derivation

高斯定律被认为是库仑定律的一个相关概念,它允许计算多种构型的电场。这个定律将在表面上形成空间的电场线关联起来,而这个空间将表面内部的电荷“Q”包围起来。假设高斯定律在库仑定律右边,表示为:

E=(1/(4∏є)0)). (Q/r2)

Where EA = Q/є0

In the aboveGauss law mathematical expression, ‘A’ corresponds to the net area which encloses the electric charge that is 4∏ r2. Gauss law is more applicable and functions when the electric charge lines are aligned in a perpendicular position to the surface, where ‘Q’ corresponds to the electric charge internal to the enclosed surface.

当表面的某些部分未在与闭合表面成直角的位置对齐时,则cosϴ的因子将被合并,当电场线与表面平行时,该因子将移动至零。在这里,封闭的术语表示表面应该没有任何类型的间隙或孔。术语“EA”表示与远离表面的总电线相关的电通量。上述概念解释了高斯法律推导.

随着高斯法律适用于许多情况,主要是有益的是在电场中存在增加对称水平时的手工计算。这些实例包括圆柱对称性和球面对称性。这高斯定律国际单位制是每个Coulomb的牛顿仪表是n m2C-1.

Gauss Law in Dielectrics

For a介电物质, the electrostatic field is varied because of the polarization as it differs in vacuum also. So, the gauss law is represented as

∇E = ρ/є0

This is applicable even in the vacuum and is reconsidered for the dielectric substance. This can be portrayed in two approaches and those are differential and integral forms.

高斯磁静磁场法

这basic concept of magnetic fields where it gets varied from the electric fields is the field lines that produce the surrounded loops. The magnet will not be observed as half to separate the south and the north poles.

其他方法是,在磁场的视图中,观察到通过封闭(高斯)表面的总磁通量似乎很简单。在内部移动到地面的内容需要变成。这使得磁静态的高斯法律可以代表为

ʃB.dS = 0 = µʃHds cosϴ = 0

这也被称为磁通量保护原理。

µcosϴʃI=0,表示ʃI=0

因此,移动到封闭表面的电流的净和是无效的。

重要性

本节对高斯法律的意义.

高斯定律对任何类型的封闭曲面都是正确的,而不依赖于物体的大小或形状。

法律的基本公式中的“Q”一词包括所有收费的整合,这些收费无论是表面内部内部的任何位置。

在这种情况下,所选表面既存在电场的内部电荷,也存在电场的外部电荷(其中,通量出现在左侧位置是因为“S”的进出端都有电荷)。

而高斯法律正确位置的因子Q'表示,在“S”内部的完整电荷。

这selected surface for the functionality of Gauss law is termed as Gaussian surface, but this surface should not be passed through any kind of isolated charges. This is due to the reason that isolated charges are not exactly defined in the electric charge position. When you reach nearer to the electrical charge, the field enhances without any boundary. While the Gaussian surface goes through the continuous charge allocation.

高斯法律主要用于对系统持有一些平衡的情况下的静电场进行更简单的静电场。这仅通过选择适当的高斯表面时加速。

总的来说,本法依赖于基于库仑法的位置的反正方形。高斯法律中的任何违约都会表示逆法的偏差。

例子

Let us consider a few高斯定律举例:

1). An enclosed gaussian surface in the 3D space where the electrical flux is measured. Provided the gaussian surface is spherical in shape which is enclosed with 30 electrons and has a radius of 0.5 meters.

  • 计算穿过表面的电量
  • 求出从表面中心到磁场距离为0.6米的电通量。
  • 知道封闭充电与电量之间存在的关系。

回答一个。

利用电通量公式,可以计算出封闭在表面的净电荷。这可以通过电子与表面上出现的整个电子的电荷倍增来实现。利用这一点,可以知道自由空间的介电常数和电通量。

Ф=Q/є0= [30(1.60 * 10-19/8.85 * 10-12]

= 5.42 * 10-12Newton*meter/Coulomb

答案b。

重新排列电通量方程,以半径表示面积,可用于计算电场。

Ф = EA = 5.42 * 10-12Newton*meter/Coulomb

E =(5.42 * 10)/A

= (5.42 * 10)/4π(0.6)2

由于电通量与封闭电荷成正比,这意味着当表面电荷增加时,通过表面的电通量也会增加。

2)。考虑一个半径为0.12米的球体,在表面上具有类似的电荷分布。该球体保持一个电场,位于0.20米的距离,其值为-10牛顿/库仑。计算

  • 计算散布在球体上的电荷量?
  • Define why or why not the electrical field which is internal to the sphere is null?

回答一个。

要了解Q,我们在这里使用的公式是

E = Q/(4∏r2є0E)

With this Q = 4∏(0.20)2(8.85 * 10-12)(-100)

Q = 4.45 * 10-10C

答案b。

在空的球形空间中,在内部存在没有电荷的电荷。由于没有内部电荷,在球体内部的电场也是空的。

高斯法律的应用

Few of the applications where this law is used are as explained as below:

  • 两个平行放置的冷凝器板之间的电场是E =Σ/∞0,其中'σ'对应于表面电荷的密度。
  • 电场强度放置在有电荷的平面薄板附近的是E=σ/2є0K and σ corresponds density of the surface charge
  • 这电场强度which is placed near the conductor is E = σ/є0K和σ对应于表面电荷的密度,当介质被选择为电介质时空气= σ/є0
  • 在具有放置在半径'R'距离的无限电荷的情况下,然后E =ƴ/2πrє0

为了选择高斯表面,我们需要考虑介电常数和电荷的比例由与电荷分布的电场对称的2D表面提供的2D表面提供的状态。在这里,这是三种各种情况:

  • 当电荷分配为圆柱对称时
  • In the case when the charge allocation is in the shape of spherically symmetric
  • 另一种情况是电荷分配在整个平面上具有平移对称性

这gaussian surface size is selected based on the condition of whether we need to measure the field. This theorem is more useful in knowing the field when there exists corresponding symmetry because it addresses the direction of the field.

这是关于高斯法律的概念。在这里,我们已经通过了解高斯法律的详细分析,其示例,重要性,理论,公式和应用程序。此外,更建议还有一个也知道高斯定律的优点高斯定律的缺点, its diagram, and others.

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